diff --git a/Lib/html/parser.py b/Lib/html/parser.py
index 5d7050dad..80fb8c3f9 100644
--- a/Lib/html/parser.py
+++ b/Lib/html/parser.py
@@ -24,6 +24,7 @@ incomplete = re.compile('&[a-zA-Z#]')
 
 entityref = re.compile('&([a-zA-Z][-.a-zA-Z0-9]*)[^a-zA-Z0-9]')
 charref = re.compile('&#(?:[0-9]+|[xX][0-9a-fA-F]+)[^0-9a-fA-F]')
+incomplete_charref = re.compile('&#(?:[0-9]|[xX][0-9a-fA-F])')
 attr_charref = re.compile(r'&(#[0-9]+|#[xX][0-9a-fA-F]+|[a-zA-Z][a-zA-Z0-9]*)[;=]?')
 
 starttagopen = re.compile('<[a-zA-Z]')
@@ -127,17 +128,25 @@ class HTMLParser(_markupbase.ParserBase):
     argument.
     """
 
-    CDATA_CONTENT_ELEMENTS = ("script", "style")
+    # See the HTML5 specs section "13.4 Parsing HTML fragments".
+    # https://html.spec.whatwg.org/multipage/parsing.html#parsing-html-fragments
+    # CDATA_CONTENT_ELEMENTS are parsed in RAWTEXT mode
+    CDATA_CONTENT_ELEMENTS = ("script", "style", "xmp", "iframe", "noembed", "noframes")
     RCDATA_CONTENT_ELEMENTS = ("textarea", "title")
 
-    def __init__(self, *, convert_charrefs=True):
+    def __init__(self, *, convert_charrefs=True, scripting=False):
         """Initialize and reset this instance.
 
-        If convert_charrefs is True (the default), all character references
+        If convert_charrefs is true (the default), all character references
         are automatically converted to the corresponding Unicode characters.
+
+        If *scripting* is false (the default), the content of the
+        ``noscript`` element is parsed normally; if it's true,
+        it's returned as is without being parsed.
         """
         super().__init__()
         self.convert_charrefs = convert_charrefs
+        self.scripting = scripting
         self.reset()
 
     def reset(self):
@@ -172,7 +181,9 @@ class HTMLParser(_markupbase.ParserBase):
     def set_cdata_mode(self, elem, *, escapable=False):
         self.cdata_elem = elem.lower()
         self._escapable = escapable
-        if escapable and not self.convert_charrefs:
+        if self.cdata_elem == 'plaintext':
+            self.interesting = re.compile(r'\z')
+        elif escapable and not self.convert_charrefs:
             self.interesting = re.compile(r'&|</%s(?=[\t\n\r\f />])' % self.cdata_elem,
                                           re.IGNORECASE|re.ASCII)
         else:
@@ -294,10 +305,20 @@ class HTMLParser(_markupbase.ParserBase):
                         k = k - 1
                     i = self.updatepos(i, k)
                     continue
+                match = incomplete_charref.match(rawdata, i)
+                if match:
+                    if end:
+                        self.handle_charref(rawdata[i+2:])
+                        i = self.updatepos(i, n)
+                        break
+                    # incomplete
+                    break
+                elif i + 3 < n:  # larger than "&#x"
+                    # not the end of the buffer, and can't be confused
+                    # with some other construct
+                    self.handle_data("&#")
+                    i = self.updatepos(i, i + 2)
                 else:
-                    if ";" in rawdata[i:]:  # bail by consuming &#
-                        self.handle_data(rawdata[i:i+2])
-                        i = self.updatepos(i, i+2)
                     break
             elif startswith('&', i):
                 match = entityref.match(rawdata, i)
@@ -311,15 +332,13 @@ class HTMLParser(_markupbase.ParserBase):
                     continue
                 match = incomplete.match(rawdata, i)
                 if match:
-                    # match.group() will contain at least 2 chars
-                    if end and match.group() == rawdata[i:]:
-                        k = match.end()
-                        if k <= i:
-                            k = n
-                        i = self.updatepos(i, i + 1)
+                    if end:
+                        self.handle_entityref(rawdata[i+1:])
+                        i = self.updatepos(i, n)
+                        break
                     # incomplete
                     break
-                elif (i + 1) < n:
+                elif i + 1 < n:
                     # not the end of the buffer, and can't be confused
                     # with some other construct
                     self.handle_data("&")
@@ -444,8 +463,10 @@ class HTMLParser(_markupbase.ParserBase):
             self.handle_startendtag(tag, attrs)
         else:
             self.handle_starttag(tag, attrs)
-            if tag in self.CDATA_CONTENT_ELEMENTS:
-                self.set_cdata_mode(tag)
+            if (tag in self.CDATA_CONTENT_ELEMENTS or
+                (self.scripting and tag == "noscript") or
+                tag == "plaintext"):
+                self.set_cdata_mode(tag, escapable=False)
             elif tag in self.RCDATA_CONTENT_ELEMENTS:
                 self.set_cdata_mode(tag, escapable=True)
         return endpos
diff --git a/Lib/test/test_htmlparser.py b/Lib/test/test_htmlparser.py
index 6a1d69335..e4eff1ea1 100644
--- a/Lib/test/test_htmlparser.py
+++ b/Lib/test/test_htmlparser.py
@@ -8,6 +8,18 @@ from unittest.mock import patch
 from test import support
 
 
+SAMPLE_RCDATA = (
+    '<!-- not a comment -->'
+    "<not a='start tag'>"
+    '<![CDATA[not a cdata]]>'
+    '<!not a bogus comment>'
+    '</not a bogus comment>'
+    '\u2603'
+)
+
+SAMPLE_RAWTEXT = SAMPLE_RCDATA + '&amp;&#9786;'
+
+
 class EventCollector(html.parser.HTMLParser):
 
     def __init__(self, *args, autocdata=False, **kw):
@@ -97,12 +109,13 @@ class EventCollectorNoNormalize(EventCollector):
 
 class TestCaseBase(unittest.TestCase):
 
-    def get_collector(self):
-        return EventCollector(convert_charrefs=False)
+    def get_collector(self, convert_charrefs=False):
+        return EventCollector(convert_charrefs=convert_charrefs)
 
-    def _run_check(self, source, expected_events, collector=None):
+    def _run_check(self, source, expected_events,
+                   *, collector=None, convert_charrefs=False):
         if collector is None:
-            collector = self.get_collector()
+            collector = self.get_collector(convert_charrefs=convert_charrefs)
         parser = collector
         for s in source:
             parser.feed(s)
@@ -116,7 +129,7 @@ class TestCaseBase(unittest.TestCase):
 
     def _run_check_extra(self, source, events):
         self._run_check(source, events,
-                        EventCollectorExtra(convert_charrefs=False))
+            collector=EventCollectorExtra(convert_charrefs=False))
 
 
 class HTMLParserTestCase(TestCaseBase):
@@ -175,10 +188,87 @@ text
         ])
 
     def test_unclosed_entityref(self):
-        self._run_check("&entityref foo", [
-            ("entityref", "entityref"),
-            ("data", " foo"),
-            ])
+        self._run_check('&gt &lt;', [('entityref', 'gt'), ('data', ' '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('&gt &lt;', [('data', '> <')], convert_charrefs=True)
+
+        self._run_check('&undefined &lt;',
+                        [('entityref', 'undefined'), ('data', ' '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('&undefined &lt;', [('data', '&undefined <')],
+                        convert_charrefs=True)
+
+        self._run_check('&gtundefined &lt;',
+                        [('entityref', 'gtundefined'), ('data', ' '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('&gtundefined &lt;', [('data', '>undefined <')],
+                        convert_charrefs=True)
+
+        self._run_check('& &lt;', [('data', '& '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('& &lt;', [('data', '& <')], convert_charrefs=True)
+
+    def test_eof_in_entityref(self):
+        self._run_check('&gt', [('entityref', 'gt')], convert_charrefs=False)
+        self._run_check('&gt', [('data', '>')], convert_charrefs=True)
+
+        self._run_check('&g', [('entityref', 'g')], convert_charrefs=False)
+        self._run_check('&g', [('data', '&g')], convert_charrefs=True)
+
+        self._run_check('&undefined', [('entityref', 'undefined')],
+                        convert_charrefs=False)
+        self._run_check('&undefined', [('data', '&undefined')],
+                        convert_charrefs=True)
+
+        self._run_check('&gtundefined', [('entityref', 'gtundefined')],
+                        convert_charrefs=False)
+        self._run_check('&gtundefined', [('data', '>undefined')],
+                        convert_charrefs=True)
+
+        self._run_check('&', [('data', '&')], convert_charrefs=False)
+        self._run_check('&', [('data', '&')], convert_charrefs=True)
+
+    def test_unclosed_charref(self):
+        self._run_check('&#123 &lt;', [('charref', '123'), ('data', ' '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('&#123 &lt;', [('data', '{ <')], convert_charrefs=True)
+        self._run_check('&#xab &lt;', [('charref', 'xab'), ('data', ' '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('&#xab &lt;', [('data', '\xab <')], convert_charrefs=True)
+
+        self._run_check('&#123456789 &lt;',
+                        [('charref', '123456789'), ('data', ' '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('&#123456789 &lt;', [('data', '\ufffd <')],
+                        convert_charrefs=True)
+        self._run_check('&#x123456789 &lt;',
+                        [('charref', 'x123456789'), ('data', ' '), ('entityref', 'lt')],
+                        convert_charrefs=False)
+        self._run_check('&#x123456789 &lt;', [('data', '\ufffd <')],
+                        convert_charrefs=True)
+
+        self._run_check('&# &lt;', [('data', '&# '), ('entityref', 'lt')], convert_charrefs=False)
+        self._run_check('&# &lt;', [('data', '&# <')], convert_charrefs=True)
+        self._run_check('&#x &lt;', [('data', '&#x '), ('entityref', 'lt')], convert_charrefs=False)
+        self._run_check('&#x &lt;', [('data', '&#x <')], convert_charrefs=True)
+
+    def test_eof_in_charref(self):
+        self._run_check('&#123', [('charref', '123')], convert_charrefs=False)
+        self._run_check('&#123', [('data', '{')], convert_charrefs=True)
+        self._run_check('&#xab', [('charref', 'xab')], convert_charrefs=False)
+        self._run_check('&#xab', [('data', '\xab')], convert_charrefs=True)
+
+        self._run_check('&#123456789', [('charref', '123456789')],
+                        convert_charrefs=False)
+        self._run_check('&#123456789', [('data', '\ufffd')], convert_charrefs=True)
+        self._run_check('&#x123456789', [('charref', 'x123456789')],
+                        convert_charrefs=False)
+        self._run_check('&#x123456789', [('data', '\ufffd')], convert_charrefs=True)
+
+        self._run_check('&#', [('data', '&#')], convert_charrefs=False)
+        self._run_check('&#', [('data', '&#')], convert_charrefs=True)
+        self._run_check('&#x', [('data', '&#x')], convert_charrefs=False)
+        self._run_check('&#x', [('data', '&#x')], convert_charrefs=True)
 
     def test_bad_nesting(self):
         # Strangely, this *is* supposed to test that overlapping
@@ -293,30 +383,20 @@ text
              'Date().getTime()+\'"><\\/s\'+\'cript>\');\n//]]>'),
             '\n<!-- //\nvar foo = 3.14;\n// -->\n',
             '<!-- \u2603 -->',
-            'foo = "</ script>"',
-            'foo = "</scripture>"',
-            'foo = "</script\v>"',
-            'foo = "</script\xa0>"',
-            'foo = "</ſcript>"',
-            'foo = "</scrıpt>"',
         ])
     def test_script_content(self, content):
         s = f'<script>{content}</script>'
-        self._run_check(s, [("starttag", "script", []),
-                            ("data", content),
-                            ("endtag", "script")])
+        self._run_check(s, [
+            ("starttag", "script", []),
+            ("data", content),
+            ("endtag", "script"),
+        ])
 
     @support.subTests('content', [
             'a::before { content: "<!-- not a comment -->"; }',
             'a::before { content: "&not-an-entity-ref;"; }',
             'a::before { content: "<not a=\'start tag\'>"; }',
             'a::before { content: "\u2603"; }',
-            'a::before { content: "< /style>"; }',
-            'a::before { content: "</ style>"; }',
-            'a::before { content: "</styled>"; }',
-            'a::before { content: "</style\v>"; }',
-            'a::before { content: "</style\xa0>"; }',
-            'a::before { content: "</ſtyle>"; }',
         ])
     def test_style_content(self, content):
         s = f'<style>{content}</style>'
@@ -324,47 +404,59 @@ text
                             ("data", content),
                             ("endtag", "style")])
 
-    @support.subTests('content', [
-            '<!-- not a comment -->',
-            "<not a='start tag'>",
-            '<![CDATA[not a cdata]]>',
-            '<!not a bogus comment>',
-            '</not a bogus comment>',
-            '\u2603',
-            '< /title>',
-            '</ title>',
-            '</titled>',
-            '</title\v>',
-            '</title\xa0>',
-            '</tıtle>',
-        ])
-    def test_title_content(self, content):
-        source = f"<title>{content}</title>"
+    @support.subTests('tag', ['title', 'textarea'])
+    def test_rcdata_content(self, tag):
+        source = f"<{tag}>{SAMPLE_RCDATA}</{tag}>"
         self._run_check(source, [
-            ("starttag", "title", []),
-            ("data", content),
-            ("endtag", "title"),
+            ("starttag", tag, []),
+            ("data", SAMPLE_RCDATA),
+            ("endtag", tag),
+        ])
+        source = f"<{tag}>&amp;</{tag}>"
+        self._run_check(source, [
+            ("starttag", tag, []),
+            ('entityref', 'amp'),
+            ("endtag", tag),
         ])
 
-    @support.subTests('content', [
-            '<!-- not a comment -->',
-            "<not a='start tag'>",
-            '<![CDATA[not a cdata]]>',
-            '<!not a bogus comment>',
-            '</not a bogus comment>',
-            '\u2603',
-            '< /textarea>',
-            '</ textarea>',
-            '</textareable>',
-            '</textarea\v>',
-            '</textarea\xa0>',
-        ])
-    def test_textarea_content(self, content):
-        source = f"<textarea>{content}</textarea>"
+    @support.subTests('tag',
+            ['style', 'xmp', 'iframe', 'noembed', 'noframes', 'script'])
+    def test_rawtext_content(self, tag):
+        source = f"<{tag}>{SAMPLE_RAWTEXT}</{tag}>"
         self._run_check(source, [
-            ("starttag", "textarea", []),
+            ("starttag", tag, []),
+            ("data", SAMPLE_RAWTEXT),
+            ("endtag", tag),
+        ])
+
+    def test_noscript_content(self):
+        source = f"<noscript>{SAMPLE_RAWTEXT}</noscript>"
+        # scripting=False -- normal mode
+        self._run_check(source, [
+            ('starttag', 'noscript', []),
+            ('comment', ' not a comment '),
+            ('starttag', 'not', [('a', 'start tag')]),
+            ('unknown decl', 'CDATA[not a cdata'),
+            ('comment', 'not a bogus comment'),
+            ('endtag', 'not'),
+            ('data', '☃'),
+            ('entityref', 'amp'),
+            ('charref', '9786'),
+            ('endtag', 'noscript'),
+        ])
+        # scripting=True -- RAWTEXT mode
+        self._run_check(source, [
+            ("starttag", "noscript", []),
+            ("data", SAMPLE_RAWTEXT),
+            ("endtag", "noscript"),
+        ], collector=EventCollector(scripting=True))
+
+    def test_plaintext_content(self):
+        content = SAMPLE_RAWTEXT + '</plaintext>'  # not closing
+        source = f"<plaintext>{content}"
+        self._run_check(source, [
+            ("starttag", "plaintext", []),
             ("data", content),
-            ("endtag", "textarea"),
         ])
 
     @support.subTests('endtag', ['script', 'SCRIPT', 'script ', 'script\n',
@@ -381,52 +473,65 @@ text
                             ("endtag", "script")],
                         collector=EventCollectorNoNormalize(convert_charrefs=False))
 
-    @support.subTests('endtag', ['style', 'STYLE', 'style ', 'style\n',
-                                 'style/', 'style foo=bar', 'style foo=">"'])
-    def test_style_closing_tag(self, endtag):
-        content = """
-            b::before { content: "<!-- not a comment -->"; }
-            p::before { content: "&not-an-entity-ref;"; }
-            a::before { content: "<i>"; }
-            a::after { content: "</i>"; }
-            """
-        s = f'<StyLE>{content}</{endtag}>'
-        self._run_check(s, [("starttag", "style", []),
-                            ("data", content),
-                            ("endtag", "style")],
-                        collector=EventCollectorNoNormalize(convert_charrefs=False))
+    @support.subTests('tag', [
+        'script', 'style', 'xmp', 'iframe', 'noembed', 'noframes',
+        'textarea', 'title', 'noscript',
+    ])
+    def test_closing_tag(self, tag):
+        for endtag in [tag, tag.upper(), f'{tag} ', f'{tag}\n',
+                       f'{tag}/', f'{tag} foo=bar', f'{tag} foo=">"']:
+            content = "<!-- not a comment --><i>Spam</i>"
+            s = f'<{tag.upper()}>{content}</{endtag}>'
+            self._run_check(s, [
+                ("starttag", tag, []),
+                ('data', content),
+                ("endtag", tag),
+            ], collector=EventCollectorNoNormalize(convert_charrefs=False, scripting=True))
 
-    @support.subTests('endtag', ['title', 'TITLE', 'title ', 'title\n',
-                                 'title/', 'title foo=bar', 'title foo=">"'])
-    def test_title_closing_tag(self, endtag):
-        content = "<!-- not a comment --><i>Egg &amp; Spam</i>"
-        s = f'<TitLe>{content}</{endtag}>'
-        self._run_check(s, [("starttag", "title", []),
-                            ('data', '<!-- not a comment --><i>Egg & Spam</i>'),
-                            ("endtag", "title")],
-                        collector=EventCollectorNoNormalize(convert_charrefs=True))
-        self._run_check(s, [("starttag", "title", []),
-                            ('data', '<!-- not a comment --><i>Egg '),
-                            ('entityref', 'amp'),
-                            ('data', ' Spam</i>'),
-                            ("endtag", "title")],
-                        collector=EventCollectorNoNormalize(convert_charrefs=False))
+    @support.subTests('tag', [
+        'script', 'style', 'xmp', 'iframe', 'noembed', 'noframes',
+        'textarea', 'title', 'noscript',
+    ])
+    def test_invalid_closing_tag(self, tag):
+        content = (
+            f'< /{tag}>'
+            f'</ {tag}>'
+            f'</{tag}x>'
+            f'</{tag}\v>'
+            f'</{tag}\xa0>'
+        )
+        source = f"<{tag}>{content}</{tag}>"
+        self._run_check(source, [
+            ("starttag", tag, []),
+            ("data", content),
+            ("endtag", tag),
+        ], collector=EventCollector(convert_charrefs=False, scripting=True))
 
-    @support.subTests('endtag', ['textarea', 'TEXTAREA', 'textarea ', 'textarea\n',
-                                 'textarea/', 'textarea foo=bar', 'textarea foo=">"'])
-    def test_textarea_closing_tag(self, endtag):
-        content = "<!-- not a comment --><i>Egg &amp; Spam</i>"
-        s = f'<TexTarEa>{content}</{endtag}>'
-        self._run_check(s, [("starttag", "textarea", []),
-                            ('data', '<!-- not a comment --><i>Egg & Spam</i>'),
-                            ("endtag", "textarea")],
-                        collector=EventCollectorNoNormalize(convert_charrefs=True))
-        self._run_check(s, [("starttag", "textarea", []),
-                            ('data', '<!-- not a comment --><i>Egg '),
-                            ('entityref', 'amp'),
-                            ('data', ' Spam</i>'),
-                            ("endtag", "textarea")],
-                        collector=EventCollectorNoNormalize(convert_charrefs=False))
+    @support.subTests('tag,endtag', [
+        ('title', 'tıtle'),
+        ('style', 'ſtyle'),
+        ('style', 'ſtyle'),
+        ('style', 'style'),
+        ('iframe', 'ıframe'),
+        ('noframes', 'noframeſ'),
+        ('noscript', 'noſcript'),
+        ('noscript', 'noscrıpt'),
+        ('script', 'ſcript'),
+        ('script', 'scrıpt'),
+    ])
+    def test_invalid_nonascii_closing_tag(self, tag, endtag):
+        content = f"<br></{endtag}>"
+        source = f"<{tag}>{content}"
+        self._run_check(source, [
+            ("starttag", tag, []),
+            ("data", content),
+        ], collector=EventCollector(convert_charrefs=False, scripting=True))
+        source = f"<{tag}>{content}</{tag}>"
+        self._run_check(source, [
+            ("starttag", tag, []),
+            ("data", content),
+            ("endtag", tag),
+        ], collector=EventCollector(convert_charrefs=False, scripting=True))
 
     @support.subTests('tail,end', [
         ('', False),
@@ -735,20 +840,6 @@ text
         ]
         self._run_check(html, expected)
 
-    def test_EOF_in_charref(self):
-        # see #17802
-        # This test checks that the UnboundLocalError reported in the issue
-        # is not raised, however I'm not sure the returned values are correct.
-        # Maybe HTMLParser should use self.unescape for these
-        data = [
-            ('a&', [('data', 'a&')]),
-            ('a&b', [('data', 'ab')]),
-            ('a&b ', [('data', 'a'), ('entityref', 'b'), ('data', ' ')]),
-            ('a&b;', [('data', 'a'), ('entityref', 'b')]),
-        ]
-        for html, expected in data:
-            self._run_check(html, expected)
-
     def test_eof_in_comments(self):
         data = [
             ('<!--', [('comment', '')]),